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This is an Accepted Article that has been peer-reviewed and approved for publication in the The Journal of
Physiology, but has yet to undergo copy-editing and proof correction. Please cite this article as an 'Accepted
Article'; doi: 10.1113/jphysiol.2014.279059.
This article is protected by copyright. All rights reserved. 0
Title: Different fixational eye movements mediate the prevention and the reversal of visual
fading
Running title: Fading prevention by fixational eye movements
Authors: Michael B. McCamy1,2
, Stephen L. Macknik1,3
, Susana Martinez-Conde1
Affiliations: 1Department of Neurobiology, Barrow Neurological Institute, Phoenix, AZ,
USA
2School of Mathematical and Statistical Sciences, Arizona State University, Tempe, AZ,
USA
3Department of Neurosurgery, Barrow Neurological Institute, Phoenix, AZ, USA
Keywords: Vision, adaptation, eye position
Total number of words (excluding references and figure legends): 7419
Table of Contents: Neuroscience - behavioural/systems/cognitive
Corresponding author: Correspondence should be addressed to Susana Martinez-Conde,
Department of Neurobiology, Barrow Neurological Institute, 350 W Thomas Rd. Phoenix,
AZ 85013, USA. E-mail: [email protected]
Key points summary:
Fixational eye movements (microsaccades, drift, and tremor) are thought to improve
visibility during fixation by thwarting neural adaptation to unchanging stimuli, but
how the different fixational eye movements influence this process is a matter of
debate.
Prior studies confounded the reversal of fading (where vision is restored after fading)
with its prevention (where fading is blocked before it happens). We found that,
whereas microsaccades are most important to reversing fading, both microsaccades
and drift help to prevent it.
This article is protected by copyright. All rights reserved. 1
Drift’s contribution to preventing fading is potentially larger than that of
microsaccades, but microsaccades prevent fading with higher efficacy than drift.
Microsaccades prevent foveal and peripheral fading in an equivalent fashion, and
microsaccadic efficacy does not depend on microsaccade size, number, or direction.
Further, faster drift may prevent fading better than slower drift
These combined findings help reconcile the long-standing controversy concerning the
roles of microsaccades and drift in visibility during fixation
ABSTRACT
Fixational eye movements (FEMs; including microsaccades, drift and tremor) are thought to
improve visibility during fixation by thwarting neural adaptation to unchanging stimuli, but
how the different FEM types influence this process is a matter of debate. Attempts to answer
this question have been hampered by the failure to distinguish between the prevention of
fading (where fading is blocked before it happens in the first place) and the reversal of fading
(where vision is restored after fading has already occurred). Because fading during fixation is
a detriment to clear vision, the prevention of fading --which avoids visual degradation before
it happens-- is a more desirable scenario than improving visibility after fading has occurred.
Yet, previous studies have not examined the role of FEMs in the prevention of fading, but
have focused on visual restoration instead. Here we set out to determine the differential
contributions and efficacies of microsaccades and drift to preventing fading in human vision.
Our results indicate that both microsaccades and drift mediate the prevention of visual fading.
We also found that drift is a potentially larger contributor to preventing fading than
microsaccades, although microsaccades are more effective than drift. Microsaccades
moreover prevented foveal and peripheral fading in an equivalent fashion, and their efficacy
was independent of their size, number, and direction. Our data also suggest that faster drift
may prevent fading better than slower drift. These findings may help to reconcile the long-
standing controversy concerning the comparative roles of microsaccades and drift in visibility
during fixation.
This article is protected by copyright. All rights reserved. 2
INTRODUCTION
When eye movements are eliminated, stationary or unchanging objects fade from
perception (Ditchburn and Ginsborg, 1952; Riggs and Ratliff, 1952 p.52; Yarbus, 1957).
Outside of the laboratory, our eyes are never still, however: even when we attempt to fixate
our gaze on an object of interest, small ocular motions, called fixational eye movements
(FEMs: including microsaccades, drift and tremor) shift our eye position. FEMs are thought
to help visibility during fixation by thwarting neural adaptation to unchanging stimuli
(Martinez-Conde et al., 2004, 2013; Engbert and Mergenthaler, 2006), but how the different
FEM types influence this process is a matter of debate. Attempts to answer this question have
been hampered by the failure to distinguish between the prevention of fading (where fading is
blocked before it happens in the first place) and the reversal of fading (where vision is
restored after fading has already occurred). There has been a relative dearth of research to
specify the oculomotor mechanisms underlying the prevention of fading.
Because fading during fixation is a detriment to clear vision, the prevention of fading
--which avoids visual degradation before it happens during fading-- is a more desirable
scenario than improving visibility after fading has occurred. Thus, determining how the
different eye movement types prevent fading is more important than establishing how they
restore visibility once fading has taken place. Yet, previous studies have not examined the
role of FEMs in the prevention of fading , but have focused on restoration instead (Martinez-
Conde et al., 2006; Troncoso et al., 2008; McCamy et al., 2012; Costela et al., 2013). It
follows that no research to date has determined the differential effects of each individual
FEM type on fading prevention, as we now do here. Recently, we developed a principled
quantitative method to determine the contribution and efficacy of microsaccades and other
eye movements to reversing fading during fixation (McCamy et al., 2012). Here we have
enhanced the method to determine the differential contributions and efficacies of
microsaccades and drift to preventing fading.
Our results indicate that both microsaccades and drift work to prevent fading. We also
found that drift is a potentially larger contributor to fading prevention than microsaccades,
although microsaccades are more effective than drift. Microsaccades moreover prevented
foveal and peripheral fading in an equivalent fashion, and their efficacy was independent of
their size, number, and direction. Our data also suggest that faster drift may prevent fading
better than slower drift. These findings may help to reconcile the long-standing controversy
concerning the comparative roles of microsaccades and drift in visibility during fixation.
This article is protected by copyright. All rights reserved. 3
METHODS
Ethics statement
Experiments were approved by the Barrow Neurological Institute Institutional Review
Board (protocol number 04BN039) and conformed to the Declaration of Helsinki. Written
informed consent was obtained from each participant.
Subjects
Seven subjects (5 males) with normal or corrected-to-normal vision participated in the
experiments. Six subjects were naive and were paid $15/session. For one subject, 2
experimental sessions were discarded due to pupil occlusion (which made the data too noisy
for accurate microsaccade detection). Three other subjects lost 5 or less trials of data, out of
256 trials, due to pupil occlusion (the eye position was lost by the eye tracker); these data
losses did not significantly affect the results.
Experimental design
Subjects rested their forehead and chin on the EyeLink 1000 head/chin support ~57
cm away from a linearized video monitor (Barco Reference Calibrator V, 75 Hz refresh rate).
The experiment consisted of 5 ~ 1-1.5 hours sessions, each including 64 randomly
interleaved trials. The first session was counted as a training session and not included in the
analyses.
Illusory fading condition. While fixating a small red spot (with a diameter of 0.05
degrees of visual angle (deg)) on the center of the screen, subjects continuously reported
whether a stimulus was faded/fading (button press) or intensified/intensifying (button release)
(Martinez-Conde et al., 2006) (Fig. 1A). To start the trial, subjects pressed a key and the
stimulus appeared on the screen. The stimulus was a two-lobe Gabor patch with a peak-to-
trough width of 2.5 deg (Gaussian standard deviations of x = 1.5 deg and y = 1 deg; sine wave
period of 5 deg; sine wave phase of 0 deg). The Gabor had a maximum contrast of 40% from
peak-to-trough and the same average luminance (50%) as the background. The Gabor was
presented at random eccentricities of 0 deg, 3 deg, 6 deg, 9 deg (measured from the center of
the fixation point to the center of the Gabor). The position of the Gabor varied randomly
across trials at one of the eight points of the compass, to control for possible contrast
adaptation effects across trials. The orientation of the Gabor also varied randomly between 0º
This article is protected by copyright. All rights reserved. 4
(here, ° represents circular angle) and 360º in each trial, to control for orientation adaptation
effects. After 30 seconds, the stimuli disappeared and the trial ended. To disregard the
potential effect of the initial stimulus onset transient at the start of each trial, we conducted
analyses only on data recorded after the first second of the trial. A minimum average of 2
transitions per 30 second trial was imposed to ensure that the subjects experienced the
illusion; one subject was discontinued after the training session due to this restriction.
Real fading condition. Experimental details were as in the Illusory fading condition;
however, the Gabor now physically faded and intensified (Fig. 1B). The Gabor always started
at 40% contrast. Then, according to the times of transitions reported by the subject in prior
randomly chosen Illusory fading trials, the Gabor faded/intensified in step fashion to a
lower/higher contrast randomly chosen from the set: 0%, 10%, 20%, 30%, 40%. To avoid
perceptual transitions due to illusory fading which might interfere with the physical
transitions, the Gabor moved at a constant speed (0.1 cycles/s) in a circular path of 1.25 deg
radius. The parameters for the movement of the Gabor were the minimal values found to
make the Gabor continuously visible at any given contrast.
Subjects performed this task well (95 ± 15% of real fadings detected; 97 ± 16% of
reports of real fading were hits), and their reaction times provided tight estimates of reaction
times in the Illusory fading condition, necessary for the contribution and efficacy analyses
(Fig. 3). The data from the Real fading trials were not otherwise subjected to additional
analyses.
<<<PLEASE INSERT FIGURE 1 AROUND HERE>>>
Eye movement analyses
Microsaccade and blink detection. Eye position was acquired noninvasively with a
fast video-based eye tracker at 500 Hz (EyeLink 1000, SR Research). EyeLink 1000 records
eye movements simultaneously in both eyes (instrument noise 0.01 deg RMS). We identified
and removed blink periods as portions of the raw data where pupil information was missing.
We also removed portions of data where very fast decreases and increases in pupil area
occurred (> 50 units/sample, such periods are probably semi-blinks where the pupil is never
fully occluded) (Troncoso et al., 2008). We added 200 ms before and after each blink/semi-
blink to eliminate the initial and final parts where the pupil was still partially occluded
(Troncoso et al., 2008). Saccades were identified with a modified version of the algorithm
This article is protected by copyright. All rights reserved. 5
developed by Engbert & Kliegl (Engbert and Kliegl, 2003; Laubrock et al., 2005; Engbert,
2006; Engbert and Mergenthaler, 2006; Rolfs et al., 2006) with = 4 (used to obtain the
velocity threshold) and a minimum saccadic duration of 6 ms. To reduce the amount of
potential noise, we considered only binocular saccades, that is, saccades with a minimum
overlap of one data sample in both eyes (Laubrock et al., 2005; Engbert, 2006; Engbert and
Mergenthaler, 2006; Rolfs et al., 2006).
Some saccades are followed by a fast and small saccadic eye movement in the
opposite direction, called dynamic overshoot, which is often more prominent in the eye that
moves in the abducting direction (Kapoula et al., 1986). Unlike the return saccade in a
square-wave jerk, a dynamic overshoot follows a saccade with very short latency between the
two movements. We identified dynamic overshoots as saccades that occurred less than 20 ms
after a preceding saccade (Møller et al., 2002) and we did not regard them as new saccades.
Instead, we added the duration of the overshoot into the duration of the saccade, thus
considering it part of the saccade. Microsaccades were defined as saccades with magnitude <
1 deg in each eye (Martinez-Conde et al., 2004). To calculate (micro)saccade properties such
as magnitude and peak velocity we averaged the values for the right and left eyes. The mean
of the median intersaccadic interval (including saccades and microsaccades) across subjects
was 285 ms (± 27 s.e.m.).
Drift periods. Drift periods were defined as the eye-position epochs between
(micro)saccades and blinks. We removed 10 ms from the start and end of each of these
epochs (because of imperfect detection of blinks and (micro)saccades), and we filtered the
remaining eye-position data with a low-pass Butterworth filter of order 13 and a cut-off
frequency of 30 Hz (Di Stasi et al., 2013). Because drifts are not generally conjugate
(Krauskopf et al., 1960; Yarbus, 1967; Martinez-Conde et al., 2004), we used data from both
the left and right eye. For instance, any given drift period had a unique maximum (mean,
standard deviation) drift speed for each eye. The values reported in Figs. 6-7 were found by
averaging all data from both eyes. The average duration of drifts across subjects was 1.11 s (±
0.19 s.e.m.). The mean maximum drift duration across subjects was 11.24 s (± 1.40 s.e.m.).
Removing filter edge effects. Before calculating drift properties (such as the mean and
maximum speed), we removed an additional 34 ms from the beginning and 110 ms from the
end of each drift period as defined above, to reduce edge effects due to the filter. We
determined that filter edge effects caused artificial increases/decreases in drift speed before
This article is protected by copyright. All rights reserved. 6
microsaccades (Fig. 6A) because we observed increases/decreases seen in the drift speed
correlation with random microsaccades (Fig. 6B). The values (34 and 110 ms) chosen were
determined by finding when the drift speed around random microsaccades (black solid line in
Fig. 6B) was first within 5% of the average drift speed (dotted horizontal line Fig. 6B). This
choice resulted in a flat correlation of drift speed with random microsaccades; thus it
removed any detectable edge effects (Fig. 6D). The removal of the edge effects due to the
filter was especially important in our analyses because microsaccade rates differ between the
two regions compared in Fig. 7. If filter edge effects had remained, we would have obtained
artificial results because the increased numbers of microsaccades would have resulted in
more instances of higher drift speeds. Finally, because we had to remove 144 ms from each
drift’s duration (34 ms from the beginning and 110 ms from the end), drifts shorter than 300
ms were not analyzed in Fig. 7A.
Removing post-saccadic drift effects. After we removed the edge effects due to the
filter, we still observed increases in drift speed after microsaccades (Fig. 6C). These are real
increases as opposed to artificial ones caused by the filter because these increases are not
seen for the correlation with random microsaccades (Fig. 6D). This agrees with recent
research reporting increased post-saccadic drift (Chen and Hafed, 2013). To analyze drift
properties without the effects of post-saccadic drift (Fig. 7B), we removed 380 ms from the
beginning of each drift (and still the 110 ms from the end for the filter edge effects) before
calculating drift properties. This value was determined by finding where the drift speed after
a microsaccade (black solid line in Fig. 6C) first equaled the average drift speed (dotted
horizontal line Fig. 6C). The correlation of drift speed with microsaccades becomes
completely flat with this choice (Fig. 6A). Finally, because we had to remove 490 ms from
each drift’s duration (380 ms from the beginning for post-saccadic drift and 110 ms from the
end for the filter edge effects), drifts shorter than 600 ms were not analyzed in Fig. 7B.
<<<PLEASE INSERT FIGURE 2 AROUND HERE>>>
Contribution and efficacy
Correlograms and notation. Let ,MX ,SX ,BX and FX denote the microsaccade,
saccade, blink, and fading report (F) stochastic onset processes, and A M S BX X X X of
all eye movements. Let *N be the number of times * occurs. Let ( )
( ) ( ) ( )AF F
j t
A
I
t j t jX X
This article is protected by copyright. All rights reserved. 7
(where ( )I t is as above), be the correlation of AX with FX , and ( 1) 1
( ) ξ ( )t w n
AF AFt wnn t
the correlogram of AX with FX (bin width w = 50 ms). We take the convention that ( )AF n
refers to the bin value of AF at bin n, and ( )AF t refers to the bin value of bin n, where wn
t w(n + 1) 1 (we adopt the same convention for any other function that is binned in time,
such as ,AFB defined below).
Contribution and efficacy development. The concepts of contribution and efficacy
have been used to measure the strength of connection between two neurons (Levick et al.,
1972; Mastronarde, 1987; Aertsen et al., 1989; Reid and Alonso, 1995; Alonso et al., 1996,
2001; Usrey et al., 1998, 1999), and recently in determining the impact of microsaccades in
restoring faded vision (McCamy et al., 2012). Here we are concerned with the impact of
microsaccades in the prevention of fading. Thus, we include no analyses concerning the
efficacy and contribution of different eye movement types to the reversal of fading
(previously reported by (McCamy et al., 2012), using this dataset). The present analyses do
not overlap with the previous analyses unless otherwise noted.
We defined the contribution of microsaccades to the prevention of fading, ( ),R M as
the percentage of fading prevention reports (R; to be defined below) caused by
microsaccades, and the efficacy of microsaccades in preventing fading, ( ),R M as the
percentage of microsaccades which caused a prevented fading report. That is:
number of s caused by microsaccades, and
total number of s( )R
R
RM
number of microsaccades which caused a .
number of microsaccades eligible to cause( )
a R M
R
R
To calculate the contribution and efficacy of microsaccades in preventing fading,
along with those of other eye movements, we estimated the number of Rs caused by
microsaccades, as well as those caused by saccades, blinks, and combinations thereof.
Because we did not ask subjects (nor could we have asked them) to report when the stimulus
was prevented from fading, we first had to take some steps to define what a report of fading
prevention was. The most crucial step to this was to find the microsaccades (and other eye
movements) that we know did not prevent fading (i.e. did not prevent an F). Importantly,
only eye movements occurring during a specific window of time in the “intensified region”
(i.e. the time in which the stimulus was reported as intensified/intensifying) did not prevent
This article is protected by copyright. All rights reserved. 8
an F. We call this window of time the “trough interval” because it corresponds to the trough
of the correlogram between eye movements and Fs, and we denote it by .
Defining the trough interval . We estimated in two steps: 1) First, we used the
distribution of the subjects’ reaction times to target fading in the Real fading condition
(which we denote by Frt) to estimate the reaction times in the Illusory fading condition. We
required to be contained within the interval [ , ]F b a (where the interval [a, b] contains
98% of the data from Frt, discarding the top and bottom 1%; Fig. 3A); we restricted to be
contained in F because eye movements in F are the only ones which did not prevent an F,
as these are the only eye movements which occurred within the reaction times of the subject.
2) We further refined 's limits as follows. Let AF be the correlogram of all eye movement
onsets (microsaccades, saccades, and blinks) with Fs. Also, let the baseline, ,AFB be the
expected value of AF assuming that the eye movements and Fs were independent
(Mastronarde, 1987; McCamy et al., 2012) (see the "Correlogram baseline and trough
interval" section below for an exact definition of the baseline; Fig. 3B). We took as the
interval of time inside of F where AF was below AFB (Levick et al., 1972; Mastronarde,
1987; Palm et al., 1988; Aertsen et al., 1989; Alonso et al., 1996; Usrey et al., 1998, 1999;
Grun, 2009; McCamy et al., 2012) and contiguous with the minimum bin closest to the Fs
(see the "Correlogram baseline and trough interval" section below for an exact definition of ;
Fig. 3B). If no bin of AF within F was significantly below AFB , we took as nonexistent
and the contribution and efficacy as zero for that subject.
Defining prevented fading reports. Having defined , we defined a report of the
prevention of fading (R) as follows. If for a given interval of time [x, y], whose duration
equals 's duration, and which is contained in the intensified region, the stimulus was not
subsequently reported as fading at some point during the interval [y, y + a], we equated that
to a subjects report, at time t = y + a, that the stimulus was prevented from fading. This
means that any given interval with 's duration inside of the intensified region occurring
before satisfies this criterion. Any interval or any interval after does not satisfy this
criterion by definition. We call the intensified region before the prevention region and
denote it by (Fig. 3B). To obtain distinct reports of fading prevention with corresponding
distinct prevention intervals, we divided the prevention region into disjoint "prevention
intervals," which we denote by ,i of the same duration as . See “Prevention and eligible
This article is protected by copyright. All rights reserved. 9
intervals” section for more details. Each i corresponds to exactly one report of fading
prevention (i.e. one R). Our goal was to estimate the number of microsaccades in the i that
caused an R.
Contribution and efficacy definitions To calculate the number of Rs caused by
microsaccades, one cannot simply add the number of microsaccades that occurred within the
,i for two reasons: 1) Some i may have contained multiple microsaccades or
combinations of microsaccades and other eye movements (i.e. blinks or saccades) (Fig. 4).
The simple addition of the number of microsaccades in all the i could thus result in some
Rs being counted as caused more than once, leading to an overestimate of microsaccadic
contribution and efficacy. 2) Some microsaccades that occurred within a i may not have
caused an R; thus, counting them as causal would overestimate their contribution and
efficacy.
<<<PLEASE INSERT FIGURE 3 AROUND HERE>>>
Multiple eye movements To account for the possibility that multiple eye movements
may have led to an R (reason 1 above), we defined the event: M = event that only
microsaccades (one or more) occurred over a time interval of duration equal to 's duration
(Fig. 4). We defined analogous events for saccades (S), blinks (B), microsaccades and
saccades (MS), microsaccades and blinks (MB), saccades and blinks (SB), and
microsaccades, saccades, and blinks (MSB) and calculated the contribution, ( ),R E and
efficacy, ( ),R E of each event E = M, S, B, MS, MB, SB, and MSB. That is, for each E, we
calculated:
number of s caused by , and
total number of s( )R
R E
RE
number of which caused a .
number of eligible to cau(
s)
e a R
R
E RE
E
The definitions of the ocular events E ensure a one-to-one correspondence between the
caused Rs and the causal ocular events within the ;i thus, the numerators of ( )R E and
( )R E represent the same quantity even though their semantics differ.
Control level To account for the possibility that some of the Es occurring within the
i may not have caused a R (reason 2 above), we estimated the number of non-causal Es
within the i from the trough interval . Es in did not prevent fading, but they were
This article is protected by copyright. All rights reserved. 10
nevertheless eligible to prevent fading because they occurred in the intensified region. We
call the probability of an E occurring within the , ( | ),P E the control level. If RN was the
total number of Rs, then the expected number of non-causal Es that occurred within the i
was estimated, using the control level, as ( | ) .RP E N
Definitions The total number of Es that occurred is ( ) ,| i RP E N thus we took the
difference between ( | ) RiP E N and ( | ) RP E N as our estimate of the causal number of Es,
i.e. the numerator of both ( )R E and ( ).R E Therefore, the contribution and efficacy of an
ocular event E are:
( | ) ( | )( | ) ( | ), a d) n( R R
R
iR i
P E N PE
E NP E P E
N
( | ) ( | )
[ ( | ) ( | )]) ,( R R
E
i RiR
E
P E N P E N NP E P E
N NE
where EN is the number of Es that were eligible to cause an R (Fig. 5). Eligible Es are those
that occurred in the intensified region before the termination of (we call this the "eligible
region" and denote it by ); Es that occurred after cannot be counted as eligible because the
subject’s perception had already changed at some point during the interval and so those Es
were not in the intensified region and were thus unable to prevent fading. We took
( | ) ,EN P E T d where d is the duration of , ( | )P E was estimated using "eligible
intervals" in the same way ( | )iP E was found (see the "Prevention and eligible intervals"
section below; Fig. 3B), and T is the amount of time spent in by the subject.
<<<PLEASE INSERT FIGURE 4 AROUND HERE>>>
Correlogram baseline and trough interval. We estimated the baseline, ,AFB using
the data from the intensified region before .F We chose this region because microsaccades
and other eye movements in this region are completely independent of the Fs as they
occurred outside of the reaction time window in both directions of time. If {0,1}J indexes
when AX is in the intensified region before ,F then we took the baseline rate to be
( ) ( ).
( )
AtA
t
X t J tr
J t
This article is protected by copyright. All rights reserved. 11
Ar is the rate at which eye movements occurred during the intensified region before F . If sn
was the amount of time in bin n, the baseline value for bin n was ( ) .AF n AB n s r Let
min ( )F
AFn
H n
(where Fn if bin n contains some time in F ) be the minimum of AF
within F . If H was significantly below AFB (Levick et al., 1972; Mastronarde, 1987; Palm
et al., 1988; Aertsen et al., 1989; Alonso et al., 1996; Usrey et al., 1998, 1999; Grun, 2009;
McCamy et al., 2012) (significance defined in the "Significance level" section below and
shown in Fig. 3B), we let 0 min{ : and ( ) }.F AFn n n n H We defined the trough
interval as all time, ,Ft contiguous with n0, such that ( )AF t was below ( )AFB t and we
denote it by . If no bin achieved significance, did not exist, and the contribution and
efficacy were taken as 0.
Significance level. We define here what it means for ( )AF n to be significantly different
from ( )AFB n . Let V be the deviations of ( )AF n from ( ),AFB n ( ) ( ),AF AFB n n in the
intensified region before F where at least 10 Fs had data going back the same duration of
time before the prior intensification occurred (this prevents the use of outliers and makes the
definition of significance more stable). Let V and
V be the mean and standard deviation of
V. We declared ( )AF n as significantly different from ( )AFB n if ( ) ( )AF AFn nB was at least
2.5 standard deviations (V) below the mean (
V) (Levick et al., 1972; Mastronarde, 1987;
Palm et al., 1988; Aertsen et al., 1989; Alonso et al., 1996; Usrey et al., 1998, 1999; Grun,
2009; McCamy et al., 2012) (Fig. 3B).
Prevention and eligible intervals. To obtain the prevention intervals ,i we divided
into disjoint intervals of the same duration as (Figs. 3B, 4). For each F, we divided the
interval of data which began at the prior intensification onset and ended at the start of into
as many disjoint adjacent segments with ’s duration as possible. The prevention interval
which was closest in time relative to a given F was always adjacent to . To avoid any bias, if
there was more than one prevention interval for a given F, the prevention interval furthest in
time from the F was randomly chosen as being adjacent to the prior intensification onset or
adjacent to the prior prevention interval. The same principle was used to find the eligible
This article is protected by copyright. All rights reserved. 12
intervals used to calculate ( | )P M , only in this case, the interval which was closest in time
relative to a given F was always (Fig. 3B).
Partitioning the microsaccadic event M. We partitioned the event M in different
ways to investigate its efficacy as a function of microsaccade magnitude, number of
microsaccades, and microsaccade direction (Fig. 8). For example, in the case of microsaccade
magnitude we defined iM as the microsaccadic event with magnitude in the interval
[0.25( 1),0.25 )i i degrees, for 1, ,4.i Notice then, i jM M for i j, and
4
1i iM M , hence the iM partition M. We also compared the efficacy of microsaccadic
events M with two or more microsaccades (denoted by 2M ) to those with one microsaccade
1( ).M Furthermore, we compared two aspects of microsaccade direction with respect to the
fading target: 1) The angle, C , between the compass position of the Gabor patch and the
direction of the microsaccade, with C varying between 0º (towards the Gabor) and 180º
(away from the Gabor). 2) The angle, O , between the orientation of the Gabor and the
direction of the microsaccade with O varying between 0º (parallel) and 90º (orthogonal).
See (McCamy et al., 2012) for an illustration of each. CiM denotes the microsaccadic event
M whose C falls in the interval [10( 1),10 )i i degrees, for 1, ,18.i OiM denotes the
microsaccadic event M whose O falls in the interval [10( 1),10 )i i degrees, for 1, ,9.i
Note,1 2{ , }M M
, 9
Oi 1{ }iM , and 18
Ci 1{ }iM also form partitions of M. To calculate the
contribution and efficacy of any event E of a given partition, we used the same from the
main analysis and applied the contribution and efficacy formulas to E. For a discussion on
how the contribution and efficacy of M relate to the contributions and efficacies of events
which partition M, see (McCamy et al., 2012).
Contribution and efficacy notes. For the contribution and efficacy analyses, we
discarded Fs when the duration of the prior intensified period was too short to contain the
entire F period (15% 6% Fs discarded). In the Illusory fading condition, the average
number of Fs ( )FN for the contribution and efficacy analyses was 334 64 Fs. For all
Illusory fading trials combined, each subject had a sufficient number of Rs to perform the
contribution and efficacy analyses; the average number of Rs ( )RN was (2999 285). To
This article is protected by copyright. All rights reserved. 13
carry out the analyses on Illusory fading trials subject to a specific condition (for instance,
only trials with the Gabor in the fovea), we required that at least 15 Fs occurred for this
condition, otherwise the measurement became noisy due to insufficient data; in that case we
took both the contribution and efficacy as nonexistent (as opposed to 0). We also included a
restriction on the number of ocular events (i.e. M, S, B etc.). That is, to measure the efficacy
of a particular ocular event E, we required that E occurred at least 12 times in the eligible
region; otherwise we took the efficacy of E as nonexistent. See Table 1 for the amount of
eligible events across subjects. Finally, because we did not consider the significance of any
ocular event E alone, we were not guaranteed that ( | ) ( | )iP E P E for each type of event
E and so in all cases (E = M, S, B, MS, MB, SB, MSB, M1, M2, etc.) we took
( |( ) max{ ) ( | ),0}R iP E P EE and ( ) max{ ( | ) ( | ),0}iR R EPE E P E N N for
each E because a negative contribution/efficacy has no meaning.
Statistical analyses
All statistical tests were two-tailed, paired t-tests. Significance levels were set at α =
0.05 and every test was corrected for multiple comparisons (where necessary) using
Bonferroni correction.
RESULTS
<<<PLEASE INSERT FIGURE 5 AROUND HERE>>>
Subjects fixated a small target on the center of a computer screen and continuously
reported, via button press, whether an unchanging visual stimulus (a 2-lobe Gabor patch with
40% contrast), presented either foveally or peripherally, was faded (or in the process of
fading) versus intensified (or intensifying) (Martinez-Conde et al., 2006; McCamy et al.,
2012) (Fig. 1A). We set out to determine the role of fixational microsaccades and drift in the
prevention of visual fading. Although previous studies have studied the roles of different eye
movement types on the restoration to visibility of already faded targets (Martinez-Conde et
al., 2006; Troncoso et al., 2008; McCamy et al., 2012; Costela et al., 2013), no research to
date has determined the relationship between the different eye movement types and the
prevention of fading (Martinez-Conde et al., 2013). One simplistic and indirect way to
determine whether microsaccades may help to prevent fading is to look at microsaccade rates
as a function of how long it took for the stimulus to fade. Here we found that microsaccade
This article is protected by copyright. All rights reserved. 14
rates increased with longer times to fading (Fig. 2). To take this a step further, and to
principally quantify the impacts of each FEM type in preventing fading, we will calculate the
contribution and efficacy of microsaccades to preventing fading, as well as the potential
contribution of drift to preventing fading.
Approach to calculating contribution and efficacy
To calculate the contribution and efficacy of microsaccades to preventing fading, we
first defined the contribution of microsaccades as the percentage of fading preventions due to
microsaccades, and the efficacy of microsaccades as the percentage of microsaccades that
prevented fading. Because we did not ask subjects (nor could we have asked them) to report
when the stimulus was prevented from fading, we first defined what a report of fading
prevention (R) was. The first step to do this was to note that if a subject’s perceptual report
was in the “intensified region” (i.e. the time in which the stimulus was reported as
intensified/intensifying) and the subject did not subsequently report fading within his/her
reaction times, then fading was prevented. The next and most crucial step was to then find the
microsaccades (and any other eye movements) that we know did not prevent fading.
Importantly, only eye movements occurring during a specific window of time in the
intensified region did not prevent fading. We call this window of time the “trough interval”,
and denote it by , because it corresponds to the trough of the correlogram between eye
movements and reports of fading (Fig. 3). The subjects’ reaction times to physical fadings
from the Real fading trials (Fig. 1B) were crucial to defining the trough interval (see Methods
for the technical definition of the trough interval) (Fig. 3). We then used the trough interval to
define reports of fading prevention in the intensified region before the trough interval. Fading
was prevented during a period in the intensified region that we call the prevention region and
denote by . The eye movements that prevented fading occurred during time intervals of the
same duration as inside the prevention region we term "prevention intervals", and denote by
i (Fig. 4). Determining these regions allowed us to estimate the contribution and efficacy of
FEMs to preventing fading.
Contribution
Our results indicate that both drift and microsaccades contribute to preventing fading.
Microsaccadic events occurred in 44% of the prevention intervals (i.e. i , the intervals
without reported transitions to decreased visibility within the subjects’ reaction times; Fig.
This article is protected by copyright. All rights reserved. 15
5A), and in only 3% of the trough intervals (i.e. , intervals preceding reports of decreased
visibility within the reaction times of the subjects). The difference between these two
quantities (41%) provides a lower bound on the contribution of microsaccades, ( ),R M to
preventing fading (Fig. 5B). That is, microsaccades caused a minimum of 41% and a
maximum of 44% of all fading preventions.
Drift is ever-present (Cornsweet, 1956), thus drift occurred in essentially every
prevention interval and every trough interval. Due to the continuous nature of drift, one
cannot determine its contribution and efficacy in the same manner as with transient eye
movements such as microsaccades, saccades, and blinks. We defined drift alone (D) as the
event that only drift occurred over an interval of time with duration equal to 's duration. The
probability of drift alone in a prevention interval i, was 52%, placing an upper bound on the
contribution of drift alone to preventing visual fading (this upper bound did not vary
significantly with eccentricity; data not shown). In other words, drift alone caused a
maximum of 52% of all fading preventions (Fig. 5A). This suggests that, whereas the
contribution of drift to the reversal of fading is small (McCamy et al., 2012), drift alone is a
large contributor to preventing fading. Thus, the low contribution of drifts to the reversal of
fading does not preclude its playing a larger role in the prevention of fading; indeed, it is
possible that drift is more important than microsaccades to preventing fading.
Efficacy
The efficacy of microsaccades, ( ),R M was 88%; that is, 88% of the microsaccadic
events that occurred during a period of intensification prevented fading (Fig. 5C). Saccadic
efficacy , ( ),R S (89%) and microsaccadic efficacy were similar (Fig. 5C). The efficacy of
any combination of microsaccades, saccades, and blinks (i.e. M, S, B, MS, MB) ranged from
87-92%, indicating that fading is rare in the presence of abrupt eye movements.
Neither the contribution nor the efficacy of microsaccades varied significantly as a
function of stimulus eccentricity (data not shown).
The efficacy of drift alone is difficult to get at, because of drift’s continuous nature. If
we simply applied our efficacy formula to drift alone, then we would get an efficacy of zero.
It could be that some drifts are better than others for preventing fading, and so it is not
appropriate to equate all drift alone events. It is important to remember that only the ocular
events that occurred within the prevention region -- but not the ocular events that occurred
within the trough interval -- prevented fading. Our results show that 97% of trough intervals
This article is protected by copyright. All rights reserved. 16
contained drift alone (i.e. 97% of fading reports were preceded by drift alone in the trough
interval), whereas only 52% of the prevention intervals contained drift alone. Thus, drift
alone was able to prevent fading in some cases, but not in others. Because of this, we
wondered whether drift alone in trough intervals was different (i.e. possibly slower) from
drift alone in the prevention intervals.
<<<PLEASE INSERT FIGURE 6 AROUND HERE>>>
Drift and microsaccades in the trough intervals vs. prevention intervals
Drift .To compare drift inside the trough to drift in the prevention region, we
compared the mean, maximum, and standard deviation of the instantaneous drift speed inside
of trough intervals to those in the prevention intervals. We analyzed only drifts that occurred
in trough/prevention intervals without microsaccades/saccades or blinks. Furthermore,
because there are higher microsaccade rates in the prevention region than in the trough
interval (Fig. 3B), edge effects due to filtering can artificially change drift speeds between the
two regions (Fig. 6B), so we made comparisons after removing the edge effects due to the
filter (see Methods; Fig. 6C-D). We found that all three parameters (i.e. mean, maximum, and
standard deviation) of instantaneous drift speed were larger on average inside the prevention
intervals than in the trough intervals (Fig. 7A), suggesting that faster drifts and drifts with
more variation in speed are better at preventing fading.
We wondered whether this result might be mainly due to increased post-saccadic drift
speeds after (micro)saccades (Chen and Hafed, 2013); Fig. 6C), To find out, we increased the
window after the beginning of the drift to get rid of the correlation of (micro)saccades (i.e.
post-saccadic drift; see Methods) and we analyzed only drift in prevention/trough intervals
that did not contain (micro)saccades or blinks. This approach ensured that the results would
not be explained by increased post-saccadic drift in the prevention region (Fig. 6C-D). In this
case, only the mean speed of drift was significantly, although moderately, faster in the
prevention intervals than in the trough intervals (Fig. 7B).
We note that removing the edge effects due to the filter was critical to our analyses,
because microsaccade rates differed between prevention and trough regions compared in Fig
7. If filter edge effects had remained, we would have obtained artificial results, because the
increased numbers of microsaccades in the prevention region would have resulted in more
instances of higher drift speeds. A similar argument applies to the post-saccadic drift. Given
This article is protected by copyright. All rights reserved. 17
that drifts seem to be faster in prevention intervals compared to the trough intervals, we
wondered whether microsaccade properties also differed between the two regions.
<<<PLEASE INSERT FIGURE 7 AROUND HERE>>>
Microsaccade magnitude, number, and direction. Because the probability of a
microsaccade occurring in the trough interval is so low (3% of trough intervals had one or
more microsaccades) we suspected that the efficacy of microsaccades would not change with
different types of microsaccadic events. Upon doing the calculations, this is mostly what we
found; that is, microsaccades were equally effective at preventing fading independent of their
size and direction (Fig. 8A,C-D). In fact, the smallest microsaccades were just as effective as
large saccades at preventing fading. This is in extreme contrast to the role of microsaccades
in reversing fading, where microsaccadic efficacy increased linearly with microsaccade
magnitude, and multiple microsaccades were more effective at reversing fading than isolated
microsaccades (McCamy et al., 2012). Here, microsaccadic events with two or more
microsaccades were slightly, but significantly, more effective than microsaccadic events with
just one microsaccade (Fig. 8B).
<<<PLEASE INSERT FIGURE 8 AROUND HERE>>>
DISCUSSION
Even when we attempt to fixate our gaze, small eye movements, called fixational eye
movements (FEMs: including microsaccades, drift and tremor) continue to shift our eye
position. Here we determined the role of FEMs in the prevention of visual fading during
fixation, for the first time, and found that both drift and microsaccades contribute to
preventing fading. Our results indicate that the contribution of drift to preventing fading is
potentially higher than that of microsaccades, but that microsaccades of any size prevent
fading with higher efficacy than drift, both in the visual periphery and in the fovea.
Microsaccades of all directions were equally effective at preventing fading, but two or more
microsaccades occurring in close succession were slightly (5%) more efficacious than single
microsaccades. We also found that drift was faster and had more variation in prevention
intervals (i.e. intervals without reported transitions to decreased visibility within the subjects’
reaction times) compared to trough intervals (i.e. intervals preceding reports of decreased
visibility within the subjects’ reaction times), but most of these differences were due to the
combination of increased post-saccadic drift speeds and higher microsaccade rates in
prevention intervals compared to trough intervals.
This article is protected by copyright. All rights reserved. 18
Our findings are compatible with a pioneering study by Gerrits and Vendrick, where
simulated drift and/or microsaccadic motions were imposed on parafoveal stimuli otherwise
stabilized on the retina (Gerrits and Vendrik, 1974). Based on qualitative analyses, the
authors concluded that “[…] the most effective eye movement to preserve vision is better
characterized by its qualities (irregularity and continuity) than by its name (drift or saccade)”
and that “[…] both the irregularity (the continuous change of direction) and the continuity of
the movement of a stimulus with respect to the retina are very important for the preservation
of perception.” Gerrits and Vendrick stressed that microsaccades were of minor importance
to visibility, however, in light of previous (albeit qualitative) work suggesting that
microsaccades were not needed to preserve foveal vision during maintained fixation. Gerrits
and Vendrick also proposed that Gaussian noise (drift) interspersed with binary noise
(microsaccades) resulted in very long periods of visibility, suggesting that the combination of
drift and microsaccades could optimize visibility during fixation, as indeed our present data
indicates. Our conclusion that microsaccades and drift both prevent fading is also consistent
with the finding (Engbert and Kliegl, 2004) that microsaccades and drift together provide
motion that is continuous (persistent on a short time scale) and irregular (anti-persistent on a
long time scale), also in line with Gerrits and Vendrick’s predictions.
Preventing vs. restoring faded vision
There has been much confusion about, and misuse of, the concepts of preventing and
reversing visual fading in the literature. Indeed, many previous papers have used both terms
as synonyms (Poletti and Rucci, 2010; Kagan, 2012) or failed to differentiate one from the
other (Nachmias, 1961; Sharpe, 1972; Kowler and Steinman, 1979). The present research
indicates that different constellations of eye movements mediate the prevention and the
reversal of visual fading during fixation. The combined results from the current study and our
previous research on the contribution and efficacy of FEMs to restoring faded vision
(McCamy et al., 2012) suggest that, whereas microsaccades are critical to counteracting
fading once it has happened, both drift and microsaccades synergistically prevent fading from
occurring. It may be that drift effectively prevents fading for a limited time only: that is, that
if a saccade, microsaccade, or blink does not interrupt the drift, then fading will occur
eventually. This notion is supported by the fact that drift alone occurred in 97% of trough
intervals: intervals preceding reports of decreased visibility within the reaction times of the
subjects. These findings may help to reconcile the long-standing controversy concerning the
comparative roles of microsaccades and drift in visibility during fixation.
This article is protected by copyright. All rights reserved. 19
Underlying physiology. Neural adaptation has been shown to occur at fast and slow
time scales (Sanchez-Vives et al., 2000a, 2000b; Wang et al., 2003) in the primary visual
cortex. One possible physiological explanation of the present perceptual results (as well as
those reported by (McCamy et al., 2012)) is that microsaccades reverse fast adaptation and
reverse/prevent slow adaptation, while drifts prevent/reverse slow adaptation. Because drift
moves visual receptive fields slowly over a small region of space, it may be that drift does not
work fast enough to reverse fast adaptation. In other words, because natural scenes are highly
correlated in space (Simoncelli and Olshausen, 2001), it follows that new stimuli brought into
receptive fields of visual neurons by drift are highly correlated to recent previous stimuli in
those same receptive fields. Conversely, because of the larger distance covered by
microsaccades, new stimuli entering the receptive fields of visual neurons will be less likely
correlated to recent stimuli. Future research should investigate the possibility that transient
signals due to microsaccades combine with sustained signals due to drifts to produce optimal
visual stimulation.
Enhancement vs. suppression. It is widely believed that microsaccades come with
elevated perceptual thresholds (Zuber and Stark, 1966; Beeler, 1967), but see (Krauskopf et
al., 1966). This elevation does not preclude a perceptual benefit of microsaccades, however.
Microsaccades act to move a visual stimulus to a new location on the retina. Once
suppression has occurred, that act can still be beneficial to perception by causing transient
stimulation, followed by increased sustained responses (enhanced by drift). Even square-
wave jerks (SWJs), which are consecutive microsaccades that occur in opposite directions
(Martinez-Conde, 2006; Chen et al., 2010; Otero-Millan et al., 2011, 2013; McCamy et al.,
2013), may be perceptually advantageous; for instance if the brief movement caused by the
first saccade, followed by the quick return to the initial position by the second saccade of the
SWJ (usually within ~200 ms), provides enough time for a brief recovery from neural
adaptation.
This article is protected by copyright. All rights reserved. 20
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ADDITIONAL INFORMATION
Competing interests
The authors declare no competing interests.
Author contributions
MBM, SLM, and SMC contributed to the conception and design of the study and to drafting
the article or revising it critically for important intellectual content. MBM conducted the data
analyses.
Funding
This study was supported by the Barrow Neurological Foundation (S.L.M. and S.M.-C.) and
National Science Foundation Awards 0852636 and 1153786 (S.M.-C.).
Acknowledgements
We thank B. Kousari for technical assistance.
TABLES
Table 1. Number of eligible microsaccadic events of a given type.
Ocular event (E) Number of subjects with
12 eligible events
Average number (±
s.e.m.) of eligible events
M 7 1424 ± 223
S 5 37 ± 21
B 6 64 ± 14
MS 6 26 ± 4
MB 6 42 ± 6
This article is protected by copyright. All rights reserved. 24
M1 (magnitude in [0, 0.25) deg) 6 295 ± 73
M2 (magnitude in [0.25, 0.5) deg) 7 860 ± 161
M3 (magnitude in [0.5, 0.75) deg) 7 296 ± 68
M4 (magnitude in [0.75, 1) deg) 6 64 ± 14
1M (one microsaccade) 7 1034 ± 143
2M ( two or more microsaccades) 7 391 ± 112
D (drift alone) 7 1932 ± 309
MC1 (C in [0 10) degrees) 7 62 ± 10
MC2 (C in [10 20) degrees) 7 76 ± 14
MC3 (C in [20 30) degrees) 7 71 ± 12
MC4 (C in [30 40) degrees) 7 88 ± 15
MC5 (C in [40 50) degrees) 7 90 ± 13
MC6 (C in [50 60) degrees) 7 85 ± 14
MC7 (C in [60 70) degrees) 7 74 ± 13
MC8 (C in [70 80) degrees) 7 78 ± 16
MC9 (C in [80 90) degrees) 7 93 ± 13
MC10 (C in [90 100) degrees) 7 93 ± 13
MC11 (C in [100 110) degrees) 7 71 ± 13
MC12 (C in [110 120) degrees) 7 71 ± 12
MC13 (C in [120 130) degrees) 7 86 ± 14
MC14 (C in [130 140) degrees) 7 108 ± 18
MC15 (C in [140 150) degrees) 7 90 ± 12
MC16 (C in [150 160) degrees) 7 82 ± 12
MC17 (C in [160 170) degrees) 7 85 ± 13
This article is protected by copyright. All rights reserved. 25
MC18 (C in [170 180) degrees) 7 71 ± 10
MO1 (O in [0 10) degrees) 7 68 ± 10
MO2 (O in [10 20) degrees) 7 134 ± 20
MO3 (O in [20 30) degrees) 7 166 ± 26
MO4 (O in [30 40) degrees) 7 221 ± 36
MO5 (O in [40 50) degrees) 7 283 ± 43
MO6 (O in [50 60) degrees) 7 220 ± 36
MO7 (O in [60 70) degrees) 7 171 ± 26
MO8 (O in [70 80) degrees) 7 142 ± 23
MO9 (O in [80 90) degrees) 7 60 ± 15
The efficacy calculations in Figs. 5C, 8 required that each subject had a minimum of twelve
occurrences per ocular event type.
This article is protected by copyright. All rights reserved. 26
1. Experimental tasks. An epoch from A, an Illusory fading trial and B, a Real fading
trial. Both panels show the physical stimulus (top row; fixation dot not to scale), the
subject’s perception of the Gabor stimulus (second row), and the subject’s report
(third row). The circular arrow around the Gabor stimulus in (B) condition indicates
that the stimulus is moving in a small circle (see Methods). Panel (A) modified from
(McCamy et al., 2012).
2.
This article is protected by copyright. All rights reserved. 27
Figure 2. Time-to-fading. Microsaccade rates (i.e microsaccades per second; N/s) as a
function of how long the stimulus took to fade, i.e. microsaccade rates for intensification
periods of varying duration. Shadow indicates the s.e.m. across subjects (n = 7).
This article is protected by copyright. All rights reserved. 28
Figure 3. The definition of the trough interval and the prevention and eligible regions.
A, One subject's reaction time distribution to physical fadings during the Real fading
condition, and F (first approximation of the trough interval) for that subject. The average
F across subjects was [−828, −289] ± [33, 10] ms. B, AF is the correlogram of all eye
movements with Fs for the same subject from (A), AFB is the baseline, and the purple interval
contained inside of F is the trough interval. See Methods for the criteria used to determine
the trough interval, as a function of the reaction times, baseline, and significance level.
This article is protected by copyright. All rights reserved. 29
Figure 4. Ocular events. Each row shows two 3-second epochs during the Illusory fading
condition from one subject. The black trace is the eye’s horizontal position. The blue and red
pulses represent the subject's perceptual reports. The purple pulse indicates the location of the
trough interval, in which ocular events did not prevent fading. The golden pulses are
prevention intervals, where fading was prevented. A green pulse indicates a detected
microsaccade, a brown pulse a saccade, and a yellow pulse a blink. Several types of ocular
events are indicated above their trough/prevention interval. M = event that only
microsaccades (one or more) occurred over a time interval of duration equal to 's duration.
Analogous events are defined similarly for saccades (S), blinks (B), microsaccades and
saccades (MS), microsaccades and blinks (MB), and ocular drift alone (D).
This article is protected by copyright. All rights reserved. 30
Figure 5. Contribution and efficacy of different ocular events to preventing fading. A,
The bars and pie chart show ( | ),P E the probability of an event E occurring within a
prevention interval, for each event E. Because ( | ) 52%,P D the upper bound on the
contribution of drift alone (D) is 52%. B, The contribution, ( ),R E of each ocular event E. C,
The efficacy, ( ),R E of each ocular event E. Error bars indicate the s.e.m. across subjects (n
= 7 for (A-B), see Table 1 for the number of subjects in each type of event in (C)). M = event
that only microsaccades (one or more) occurred over a time interval of duration equal to 's
duration (Fig. 3). Analogous events are defined similarly for saccades (S), blinks (B),
microsaccades and saccades (MS), microsaccades and blinks (MB), and ocular drift alone
(D).
This article is protected by copyright. All rights reserved. 31
Figure 6. Instant drift speed correlations with microsaccades and random
microsaccades. A-B, Instant drift speed around microsaccades (A) and random
microsaccades (B) with 10 ms windows removed from the beginning and end of each drift.
The changes in drift speed around the time of random microsaccades (decreases prior to and
increases after) are due to the edge effects of the filter. C-D, Instant drift speed around
microsaccades (C) and random microsaccades (D) with 34 ms removed from the beginning
and 110 ms removed from the end of each drift; thus removing the edge effects due to the
filter. Shadows indicate the s.e.m. across subjects (n = 7).
This article is protected by copyright. All rights reserved. 32
Figure 7. Drift properties inside prevention vs. trough intervals, with and without the
effects of post-saccadic drift. Drift speed properties in prevention vs. trough intervals, A,
with, and B, without, the effects of post-saccadic drift. Shadows and error bars indicate the
s.e.m. across subjects (n = 7). * indicates statistical significance with p < 0.05 and **
indicates statistical significance with p < 0.01 (two-tailed, paired t-test). Error bars indicate
the s.e.m. across subjects (n = 7).
This article is protected by copyright. All rights reserved. 33
Figure 8. Microsaccade magnitude, number, and direction. A, The efficacy of
microsaccadic and saccadic events did not vary significantly with magnitude. iM denotes the
microsaccadic event M whose magnitude falls in the interval [0.25( 1),0.25 )i i degrees, for
1, ,4.i B, Microsaccadic events M with two or more microsaccades 2( )M
were slightly,
but significantly, more efficacious than events with one microsaccade 1( )M . C, The efficacy
of microsaccades did not vary as a function of their direction relative to the compass position
of the Gabor. C is the angle between the microsaccade direction and the compass position of
the Gabor. CiM denotes the microsaccadic event M whose C falls in the interval
[10( 1),10 )i i degrees, for 1, ,18.i D, The efficacy of microsaccades did not vary as a
function of their direction relative to the orientation of the Gabor. O is the angle between the
microsaccade direction and the orientation of the Gabor. OiM denotes the microsaccadic
event M whose O falls in the interval [10( 1),10 )i i degrees, for 1, ,9.i Error bars
indicate the s.e.m. across subjects; see Table 1 for the number of subjects in each type of
event. * indicates statistical significance with p < 0.05 (two-tailed, paired t-test).